Hello Christine.
First off I want to go over the 4Kx2k HDMI 4 port splitter and state all this device does is take a single video source and reproduce that source on all 4 monitors. What is your goal using this splitter as all it is doing is showing the same display on 4 screens.
Winkey+R will resolve your issue where you stated “I can see the laptop screen on the monitors; however in setting up the display, only see one monitor (laptop) and that screen is duplicated on the other external monitors.”
I recommend first connecting a monitor directly to your laptop via HDMI, going into your display options and see if the monitor shows up in the display properties, if not please attempt a reboot, if it still does not show up please attempt updating your graphic drivers.
Depending on the input of your monitors, to get a 3RD display going you will need to utilize the USB-C connector or the USB SS connector.